(a) Here the Gemara discusses the idea that R' Eliezer freed his Eved in order to count him for a Minyan. Even though there is an Issur involved in doing so, since it is for a Mitzva, it would be allowed.
The Gem. then brings up the question that this would constitute a Mitzva Habo B'Aveirah, and answers that it would be allowed since it is a Mitzva D'rabim.
My question is, isn't ''Mitzva Habo B'Aveirah'' applicable when both the Mitzva and the Aveirah come about simultaneously? Here, the freeing of the Eved took place first and only then could the Minyan take place, afterwards.
(b) This is unrelated to the above. I am trying to locate the Sugya which contains a statement of Rabbi Akiva that ''cherished are afflictions''?
If you or one of the other kollel members could direct me where in Shas this appears, I would greatly appeciate it.
The rule you are mentioning applies to Aseh Docheh Lo Ta'aseh and not to Mitzvah ha'Ba'ah ba'Aveirah.
With regard to Mitzvah ha'Ba'ah ba'Aveirah, we find in Tosfos (Sukah 30a) Mitzvah ha'Ba'ah ba'Aveirah means that (1) the Mitzvah is only accomplished because of the Aveirah (which is true in our case), and (2) if the effects of the Aveirah are still felt at the time that the Mitzvah is performed, or at the time that the object which is used for the Mitzvah (which, in our case, is the freed man) becomes available for the Mitzvah.
The RITVA (Sukah ibid., Pesachim 35b and Rosh Hashanah 28a, see Insights to Sukah 30:1) proves from the Yerushalmi that the principle of "Mitzvah ha'Ba'ah b'Aveirah" applies only when the performance of the Mitzvah itself causes one to transgress an Aveirah . For example, by making an animal that belongs to someone else a Korban or by designating someone else's branch as a Lulav, one acquires the object through changing the name of the animal (Shinuy ha'Shem) into a "Korban" or changing the name of the branch into a "Lulav," and thereby transgresses the Isur of stealing. That is not necessarily true in this case, since the Shtar Shichrur made the slave free, and not the Mitzvah.
Accordingly, the expression "Mitzvah ha'Ba'ah ba'Aveirah" may be seen as a borrowed term. The Gemara really means to ask, "How could he do an Aveirah and free the slave, even if he intended to count him for a Minyan? It is not permitted to do an Aveirah even if it can later bring about a Mitzvah!"
M. Kornfeld